Droop controlled inverters are widely used in islanded microgrids to interface distributed energy resources and to provide for the loads active and reactive powers demand. In this scenario, an important issue is to assess the stability of the microgrids taking into account the network and currents dynamics that are also affected by the control parameters. This paper shows how a dynamic phasor approach can be used to derive a closed loop model of the microgrid and then to perform an eigenvalues analysis that highlights how instabilities arise for suitable values of the frequency droop control parameter. Further, it is shown that the full order system is well approximated by a reduced order system which captures the inverters phase and line currents dynamics.